Skip to main content

TS

Proof pearl: Bounding least common multiples with triangles

Authors

Joseph Chan and Michael Norrish

Australian National University

NICTA

Abstract

We present a proof of the fact that 2^n ≤ lcm{1 . . . (n + 1)}. This result has a standard proof via an integral, but our proof is purely number theoretic, requiring little more than list inductions. The proof is based on manipulations of a variant of Leibniz’s Harmonic Triangle, itself a relative of Pascal’s better-known Triangle.

BibTeX Entry

  @inproceedings{Chan_Norrish_16,
    publisher        = {Springer},
    isbn             = {9783319431437},
    author           = {Chan, Joseph and Norrish, Michael},
    month            = {aug},
    slides           = {http://www.nicta.com.au/pub-download/slides/9267},
    editor           = {{Jasmin Christian Blanchette and Stephan Merz}},
    year             = {2016},
    title            = {Proof Pearl: Bounding Least Common Multiples with Triangles},
    booktitle        = {International Conference on Interactive Theorem Proving},
    pages            = {140--150},
    address          = {Nancy, France}
  }

Download